Can this be a dry vent for a lower level bathroom?

[superboer08]

I am wondering if I can use the same vent stack from the kitchen sink to also vent a new bathroom in the level below this kitchen. The kitchen is not exactly an island vent, but I could do something like what is shown for the point of the question. The red line would be where I would add a vent line for the basement. So I think it would still be a dry vent, but I’m not sure?

Thanks,
Jon